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Possibility in physics, the relevance to
quantum mechanics
Olimpia Lombardi
CONICET – University of Buenos Aires
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90 years of uncertainty
Uncertainty?Undetermination?
The position and the velocity of an object cannot both be measured exactly, at
the same time, even in theory
impossible?
It’s time to think about the concept of possibility
in quantum mechancis
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Content
Basic modal intuitions
Subjective vs objective possibility
Actualism vs possibilism
Possibility and probability
Possibility in physics
Possibility in quantum mechanics
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Content
Basic modal intuitions
Subjective vs objective possibility
Actualism vs possibilism
Possibility and probability
Possibility in physics
Possibility in quantum mechanics
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Basic modal intuitions
Middle Ages true judgementsnecessary
contingentmodes of truth
Modality
Concepts involved in modal discourse:
Possible: X
Necessary: X= X
Impossible: X
Contingent: X= X
Possibleactual
non-actual
XX : whatever is actual is possible
XX : whatever is necessary is actual
X
actual X
non-actual X
X
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Content
Basic modal intuitions
Subjective vs objective possibility
Actualism vs possibilism
Possibility and probability
Possibility in physics
Possibility in quantum mechanics
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Subjective vs objective possibilities
What the predicate ‘possible’ is applied to?
Semantic
propositions
Subjective
beliefs
S p ⊬S p
S p ├S p
A p EA (p)
Objective
states of affairs
Actualist
Possibilist
De dicto
judgements
De re
ontic items
Abelard XII century
Possible
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Content
Basic modal intuitions
Subjective vs objective possibility
Actualism vs possibilism
Possibility and probability
Possibility in physics
Possibility in quantum mechanics
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Actualism vs possibilism
Actualism: Everything that is real is actual
Diodorus Cronus: “the possible is that which either is or will be”
Bertrand Russell: “possible means sometimes, necessary means always”
Reduces possible to actual
Actuality and possibility are coextensive
Chrysippus : “even thought something is not true and may never be true,
it may nevertheless be possible”
There are possible states of affairs that never become actual
Actuality is a subclass of possibility
Possibilism: Not everything that is real is actual
Philo of Megara : “possible is that which is capable of being true by the
proposition’s own nature”
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Actualism vs possibilism
XX Century: actualism prevails
Popper: “scientific” concept of determinism,“the doctrine that the state
of any closed physical system at any given future instant of
time can be predicted, even from within the system, with any
specified degree of precision”
influence of
logical-positivism
verificationist theory of meaning
Problem of determinism
Russell: “a system is said ‘deterministic’ when, given certain data e1, e2,
..., en at times t1, t2, ..., tn respectively, concerning this system,
if Et is the state of the system at any time t, there is a functional
relation of the form Et = f(e1, t1, e2, t2,..., en, tn).”
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Content
Basic modal intuitions
Subjective vs objective possibility
Actualism vs possibilism
Possibility and probability
Possibility in physics
Possibility in quantum mechanics
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Possibility and probability
Frequentist relative frequencies
Probabilitymeasure of the degree
of belief of a rational
agent
Subjective
(Bayesianism-ignorance)
Logical
(a priori)
Objective
Propensivist measure of an objective
tendency, propensity,
potentiality, disposition
Possibility Subjective
Semantic
ObjectiveActualist
Possibilist
probability is a mathematical concept
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Content
Basic modal intuitions
Subjective vs objective possibility
Actualism vs possibilism
Possibility and probability
Possibility in physics
Possibility in quantum mechanics
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Possibility in physics
Objective possibility: What is not prevented from happening by X
?
Logically
possible
Metaphysically
possible
Physically
possible
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SoAsT
Possibility in physics
A state of affairs (SoA) is physically possible iff it is not prevented
by a physical theory T from happening.
A particle moves at a velocity v>c
possible in CM
impossible in SR
A photon moves at a velocity v=c necessary in QFT
Physically
possible
Physically
impossiblePhysically
necessary
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Possibility in physics
Conditional possibility: (SoA1/SoA0).
Synchronic: Thermodynamics PV/T=k
SoA1 : “the gas has a pressure P1 and a temperature T1
SoA0 : “the gas is confined in a volume V1
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Possibility in physics
Conditional possibility: (SoA1/SoA0).
Diachronic: Classical physics
SoA1 : “the body is in state s1 at time t1
SoA0 : “the body is in state s0 at time t0
Determinism:
Indeterminism:
Actualism: given SoA1 actual, the actualist cannot say if it is
conditionally necessary or not
(SoA1/SoA0), and also (SoA1/SoA0)
(SoA1/SoA0), but ¬ (SoA1/SoA0)
(reduction of indeterministic evolutions to underlying deterministic dynamics)
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Possibility in physics
Probability in physics:
It does not apply to necessary or impossible SoAs
Reference class: possible but not necessary SoAs
Pr(SoA)=1 does not mean necessary
Pr(SoA)=0 does not mean impossible
In general, probability conditional to another SoA
Frequentism prevails over propensivism
(influence of logical positivism)
(when all the probabilities are conditioned on the same SoA,
conditionalization can be put into parenthesis)
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Content
Basic modal intuitions
Subjective vs objective possibility
Actualism vs possibilism
Possibility and probability
Possibility in physics
Possibility in quantum mechanics
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Possibility in quantum mechanics
Copenhagen & GRW: indeterminism, but probabilities always
referred to measurements (frequentism)
Bohmian mechanics: determinism and subjective probability
Many worlds: determinism, actualist
QBism: subjective probabilities
Wave function realism: the wave function is a concrete field
of matter
Subjective or Objective-actualist
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Possibility in quantum mechanics
Challenge: interpretation based on an objective possibilist view of
possibility and probability
Given an observable, it has possible values:
only one is actual
the remaining may never become actual
“Quantum state realism”: | measures propensities as real as actualities
Reality unfolds into two realms: possibility and actuality
In Aristotelian terms: “being can be said in different ways:
as possible being or as actual being”
This explains how non-actual possibilities may have effects on actuality
“Non-interacting experiments”
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Possibility in quantum mechanics
There are at least two interpretations of QM of this sort:
The Modal-Hamiltonian Interpretation
(Olimpia Lombardi & Mario Castagnino)
The Transactional Interpretation
(Ruth Kastner, based on John Cramer)
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